Published 2011
| Published
Book Section - Chapter
Open
Stable W-length
- Creators
- Calegari, Danny
- Zhuang, Dongping
- Others:
- Jaco, William H.
- Li, Weiping
Abstract
We study stable W-length in groups, especially for W equal to the n-fold commutator γ_n := [x_1, [x_2,...[x_(n−1), x_n]]....We prove that in any perfect group, for any n ≥ 2 and any element g, the stable commutator length of g is at least as big as 2^(2−n) times the stable γ_n-length of g. We also establish analogues of Bavard duality for words γn and for β_2 := [[x, y], [z,w]]. Our proofs make use of geometric properties of the asymptotic cones of verbal subgroups with respect to bi-invariant metrics. In particular, we show that for suitable W, these asymptotic cones contain certain subgroups that are normed vector spaces.
Additional Information
© 2011 American Mathematical Society. We would like to thank Frank Calegari, Benson Farb, Denis Osin and Dan Segal for helpful comments. We would also like to thank the anonymous referee for a very careful reading and for catching several errors. Danny Calegari was supported by NSF grant DMS 1005246.Attached Files
Published - Calegari2011p17414.pdf
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Additional details
- Eprint ID
- 29763
- Resolver ID
- CaltechAUTHORS:20120319-082257258
- DMS 1005246
- NSF
- Created
-
2012-03-19Created from EPrint's datestamp field
- Updated
-
2021-11-09Created from EPrint's last_modified field
- Series Name
- Contemporary Mathematics
- Series Volume or Issue Number
- 560